Appunti behavioural economics

Behavioural economics

Individual behaviour and consumer behaviour

Fully rational firm behaviour in front of boundedly rational behaviour: the idea is that firms can naturally exploit the limits of rationality by consumers. Firms are made by people, who have similar limits to rationality as consumers.

Everyday activities and cognitive systems

There are two lists of everyday activities. On the left: understanding that one object is closer than another one, answering a calculation, driving the car or understanding simple sentences. On the right: giving somebody your phone number, answering a calculation, parking in a limited space or reading “Behavioural Economics”. These activities have common elements: the general idea from a cognitive perspective is one of the leading approaches, that is System 1 vs System 2.

Thinking fast and slow, Daniel Kahneman: He summarizes the idea behind System 1 vs System 2. They are two systems that characterize our brain activity:

• System 1: Mostly involved for the activities on the left. It is fast, almost automatic, and effortless or with limited effort. It’s the system for simple operations.
• System 2: Another cognitive system involved in mental activities like the ones on the right. It is slow, deliberate (we want to make), effortful (it requires cognitive resources).

System 2 intervenes when System 1 is not enough, but at a cognitive cost. We don’t want to use System 2 too frequently, since it is effortful. Individuals are characterized by what are called biases: systematic errors (our errors are predictable). We can study these biases, but when they are made by consumers, firms can exploit them, and consumers can try to make corrections to their behaviour.

Optical illusions and decision-making

Optical illusions: System 1 gives the person a first reaction. System 1 is the system which acts in an automatic way, so it’s using the inputs from the outside world to produce an impression. Here is the conflict between System 1 and System 2. System 1 (perceptions, impressions) has an impact on how people take decisions and behave. Some experimental evidence shows that System 1 is important, also to understand our own behaviour (what we do and what we don’t).

Microeconomics concepts

The traditional approach

• Consumers have preferences or tastes. E.g., two goods: apples and bananas. A basket is a combination of the two goods. Consumers have preferences over baskets, so given a combination of the two, they can say if they prefer one basket to the other (E > E’), or they are indifferent (E – E). If they can compare them, they have complete preferences, so any pair of baskets can be ranked by the consumer.
• The preferences are transitive: if I prefer E to E’ and E’ to E’’, E is preferred to E’’ (transitivity).
• Non-satiation: consumers are always happier with a higher quantity of a good.

Rationality means preferences that are complete and transitive.

Utility and budget constraints

Utility: if preferences are rational, then we can represent them through what we call the utility function. If we prefer one basket to the other, then the utility associated with the first basket is higher than the utility associated with the second one. Utility is important not because individuals have utility functions in mind, but because it’s a convenient way to represent preferences (complete and transitive). If you believe that individuals have these preferences, then you can represent them through the utility functions. You don’t need to think that you have the utility function in mind. In order to buy goods, you need to pay a price (you can have all the baskets you can afford). Then, the budget constraint must be no more than the income.

Suppose that we have a fully rational consumer. Full rationality means complete and transitive preferences, which implies that we can talk about the utility function. If we have a utility function, we can talk about the indifference curves: they are the set of baskets having the same utility, so they are judged as indifferent by the consumer. The utility is the same if and only if the consumers are indifferent. If we collect all the points associated with a given developed utility, we have an indifference curve.

In the graph, there are two indifference curves: one for the level u=20 (utility of 20) and one for u=10. These numbers don’t have a content. If u=20, the consumer is happier than the other, since consumers prefer baskets associated with an indifference curve of u=20. If the indifference curve is higher (E’’), then the utility is higher. In u=10 there are two points (E, E’’) judged as indifferent by the consumers. On the two axes, there is A and B (the quantity of good A and the quantity of good B).

Suppose we start from point E and then we start reducing the quantity of good B, but at the same time, we want to keep the utility fixed. We need to increase the quantity of good A since consumers are happier when they have more of a good. In order to remain on the same indifference curve, we need to increase the quantity of A. How much do we need to increase? This depends on the consumer’s preferences. To what extent can A and B be considered as substitutes? The more you move upward, the higher the utility. E’’ is preferred to both E’ and E. The budget constraint is the straight line. Vertical intercept: I/Pa (the quantity of A that I can buy if I spend all my income on A). I/Pb (the quantity of B that I can buy if I spend all my income on B). E’’ is on the indifference curve as high as possible but also on the budget constraint. It’s the preferred basket that you can buy. Given your preferences, given the prices (the consumer does not choose the price) and the income, the fully rational consumer is choosing E’’. The consumer maximizes the utility: he is looking for a basket on the highest indifference curve and on the budget constraint. If we want to buy only A (B=0), the quantity we can buy is I/Pa, the income divided by the price is the quantity we can buy of A if we buy only A.

C’è un errore nel grafico (P’a va sopra a Pa).

Connection between optimal choice and individual demand function

The relationship between the quantity demanded by the consumer and the price of the good. If the consumer faces different prices (Pb, income, and preferences remain the same since preferences are not affected by price, they are exogenous). When we have different prices, we don’t change our preferences, but our choices.

What is the optimal choice? Optimal solutions for two different prices (Pa, P’a). The vertical intercept of I/Pa is above I/P’a: P’a is higher. If the price is higher, the quantity of the good that can be bought is lower (the law of demand). Pa vs P’a means comparing optimal choices for different prices. As a result, the optimal choice by the consumer is different (it moves from E’’ to E’). The quantity of good A is lower, as well as the quantity of good B.

On the left: for the two prices (Pa, P’a) we have the quantity demanded. The demand function is something that in the standard approach can be derived from fully rational behaviour of consumers. Consumers maximizing utility leads to quantity demanded (every time the price is different, the consumer can compute different optimal choices). The only goods for which higher prices mean higher quantity: Giffen goods.

We can derive the demand functions from preferences. On the right: graphic representation of optimal choices. The price of good A is different, budget constraint given by the straight line that corresponds to a price (Pa). The vertical intercept is the amount of good A that can be bought when the price is Pa (and all the income is spent on A). The consumer wants to maximize his utility, given the budget constraint and his preferences. There is an indifference curve for any level of utility. The optimal choice is point E’’, the tangency between the indifference curve and the budget constraint. E’’ is a combination of A and B given the price. Pa is the quantity demanded for good A for the price Pa. In order to find all the points on the line of the graph (l’ipotenusa sulla sinistra) on the left, you need to find the optimal choice for every possible price.

Demand is something we can measure. Preferences can be measured as well, but it’s more complicated. The demand results from the process of optimal choice.

Elasticity of demand

Elasticity of demand: the measure of how demand is sensitive to price variation. Once we change the price, we expect a change in demand. How much? It depends on the properties of the demand function, which in turn depend on preferences. Formally, elasticity is defined as the ratio between the percentage variation of demand and the percentage variation of price causing the percentage variation of demand. It’s calculated with a “–” in front of it because elasticity becomes positive (scelta di convenienza, se non metti il – l’elasticità è sempre negativa). If the demand is downward, positive variations of price lead to a negative variation of quantity and vice versa. If there is a variation of 5% in price, how is the quantity of demand reacting? It clearly slows down by, for example, 20% the elasticity is 20/5= 4%. Advantage of the method: since we are using percentages, elasticity does not depend on the unity of measure. Demand elasticity is affected by preferences:

• Substitute goods: If the consumer has a lot of alternatives, the elasticity tends to be higher (if there is an increase in price, the consumer can go and buy something different).
• Fraction of income: The higher it is, the higher the elasticity of demand tends to be. 80% of the income to go to McDonald, if McDonald’s increases the price, you tend to spend less.

Elastic: price variations are very important. The higher the elasticity, the higher the demand is elastic. Unelastic: not elastic.

Gains, losses and reference points

The standard rationality approach is related to the role that gains, losses and reference points have in decision making. What are the objects of preferences, and where do the preferences come from?

Reference points

The research started by asking people simple questions and comparing the answers to the standard approach in economics. The intuition is that Carol is getting poorer (from 4 million to 3 million), Amanda is getting richer (1 million to 1.1 million). The answer to the question depends on the argument in the utility function, or on what preferences are defined. Utility is the absolute value of wealth. In absolute terms, Carol should be considered happier because in the end, she has 3 million (higher utility). However, for people, not only absolute evaluations are important, but also relative. So, preferences are not only defined on absolute quantities but also in terms of relative quantities.

From a mathematical point of view, in addition to the utility function, we can add a value function, which is an increasing function (the higher the argument of the function, the happier the person). The value function measures the utility of an outcome (x) with respect to a reference point (r: the standard of comparison, compare X with respect to R: x and r have the same unity of measure). Reference-dependent utility function is given by:

u’ (x) (the absolute evaluation, the standard utility) = pu(x) + v(x-r) (relative evaluation).

p (rho) is a positive parameter (the higher its value, the more the absolute evaluation is important).

• Gain: An outcome above the reference point.
• Loss: An outcome below the reference point.

Individuals tend to be loss averse: individuals dislike losses more than they like gains of the same level. V(x-r) is an increasing function. Assume a fixed positive quantity G (the variation in income, or the quantity of good). Mathematically, v(-g) is smaller (<) than -v(g). v(-g) is a loss of amount g, in general, would be smaller than -v(g): the increasing utility due to the gain, which becomes a negative quantity. If I consider a loss of 10, the reduction in value would be higher than the increase in value associated with a gain of 10.

Reference points are produced by a combination of factors (some of them are affected by System 1):

• History: e.g., Amanda and Carol (the reference point was the initial wealth, the starting point), past purchase experience.
• Expectations: e.g., new goods. If the good is new, then it’s difficult to have a past experience. The individual has to make some expectations on quality (coming from objective and subjective aspects like advertising).
• Framing effects: With only two alternatives, we cannot talk about rationality. Any preference can be considered as rational. If we prefer no risk, plan A would be the most suitable. If you are risk-averse, don’t go for B.

Most people tend to choose D. There is no wrong answer (it’s a matter of preferences), however, the two questions have a different formulation of the same choice: A=C (200 saved and 400 die) and B=D (in terms of the probability of the two outcomes). In A and B the question is expressed in terms of gain, and in loss in the second version. If you ask a question in terms of losses, people tend to avoid option C, where a lot of persons are dying. The idea is that individuals tend to be risk-averse when in front of gains and risk lovers when losses are involved. This is an example in which the reference point is manipulated by the framing. Whenever you can have control of a reference point, you can influence the decision of the individual towards certain directions. Ex. sales (saldi): it is compulsory to express the initial price and the percentage variation. This is thought to be in favour of the consumer, but at the same time, it can also be used to modify the preferences. If the consumer didn’t know the initial price, he wouldn’t be aware of his gain. Even if the final price was the same, irrational consumers should be affected only by the final discounted price (without giving any importance to the initial price).

Choice with risk

• Situation of uncertainty: where the individual’s lack of certainty comes from the fact that the individual is unaware of the possible outcomes, or even if he knew it, he couldn’t access the probabilities of the various outcomes. These probabilities either do not exist or are not known by the individual.
• Situation of risk: when individuals know the possible outcomes and the corresponding probabilities. A complete knowledge of what can happen. Ex. the roulette: we know that the outcomes are equally likely.

This is a situation of risk: the probabilities are objective and known by Alan. The probability that the car is stolen is 0.05, that he is stopped by police is 0.10, that there is no theft, no accident and no police is 0.80. All of these events are incompatible (either his car is stolen, or he has an accident), only one can happen. This is the way in which the decision process can be represented. The rows report the level of final wealth in three possible situations corresponding to the insurance Alan chooses (full insurance, theft, no insurance). The columns are associated with the possible outcomes subject to probabilities (theft, accident, police, no theft – accident – police). Ex. with full insurance: protected against any risk, he has to pay 9 (so 20-9= 11), but he can earn 50 because if anything happens to his car, he can be refunded 50 euros (the value of the car) = 61.

With insurance against theft: 14 euro if the car has an accident because he pays 6 (20-6=14), but if the car has an accident he loses the value of his car (there is no money back), so you remain with 14 euro. No insurance: if nothing happens, he gets 70.

By looking at the full row, you have the prospect: a sequence of possible outcomes to which we associate probabilities and depend on what we do. The outcomes of our decisions are not numbers, but prospects (outcomes with a certain probability, which depends on the situation). Defining prospects instead of outcomes can help define a decision under risk.

Utility function

Utility function u(x) over wealth: the utility of a prospect is the expected utility of the wealth outcomes. If you want to associate a number to a prospect, you need to compute the expected value of the utility associated with each outcome. Then, you multiply the utility for the probability of that outcome, and you sum up. Rational individuals should choose the prospects with the highest expected utility. U(A), V(A) = expected value of the prospects (probability x the outcomes). The expected utility U(A) vs the expected value of the prospect V(A): YOU MULTIPLY THE PROBABILITY X THE OUTCOMES, NOT DIRECTLY X THE UTILITY. The expected utility = the utility of the outcomes, the expected value of a prospect is just the average value (probabilities x outcomes). Depending on your preferences (u), you can make different choices.

Ex. U(X) = x (the utility is the outcomes) U(x) = √x U(x) = x² /50

For all these possible utility functions, we can compute the expected utility associated with each possible choice. The optimal choice is the choice given the highest expected utility. If the individual has a linear utility function, the optimal is the insurance for theft (partial). If the utility is √x, the highest expected utility is the full insurance, whereas with x² /50 the optimal is no insurance. The consumer has certain preferences, and then you pick up the option with the highest expected utility. You can only compare in a given row, not across rows because these preferences are not made to express evaluation across individuals. In this context, they can only be used to make predictions about the choices of a specific individual.

Look at these numbers in relative terms, not absolute. Prendere ogni fila e inserirla in questa definizione: Probabilities and outcomes are the same for all the alternatives, but the numbers are different because of the different utility functions. In the linear case, where the utilities are the outcomes directly, the expected utility with full insurance is 61, because you always get 61. Whereas, the expected utility with no insurance is (20 x the probability of 0.05) + (20 x 0.05) + (30 x 0.10) + (70 x 0.80).

Each case is expressing three important situations regarding the attitude towards risk:

• The linear case is a situation where the individual is called risk neutral (not risk averse nor risk lover).